Simulation and the monte carlo method

Nonlinear Oscillations: Exact Solutions and their Approximations

High-Performance Piezoelectric Energy Harvesters and Their Applications

The last two decades have witnessed several advances in microfabrication technologies and electronics, leading to the development of small, low-power devices for wireless sensing, data transmission, actuation, and medical implants. Unfortunately, the actual implementation of such devices in their respective environment has been hindered by the lack of scalable energy sources that are necessary to power and maintain them. Batteries, which remain the most commonly used power sources, have not kept pace with the demands of these devices, especially in terms of energy density. In light of this challenge, the concept of vibratory energy harvesting has flourished in recent years as a possible alternative to provide a continuous power supply. While linear vibratory energy harvesters have received the majority of the literature’s attention, a significant body of the current research activity is focused on the concept of purposeful inclusion of nonlinearities for broadband transduction. When compared to their linear resonant counterparts, nonlinear energy harvesters have a wider steady-state frequency bandwidth, leading to a common belief that they can be utilized to improve performance in ambient environments. Through a review of the open literature, this paper highlights the role of nonlinearities in the transduction of energy harvesters under different types of excitations and investigates the conditions, in terms of excitation nature and potential shape, under which such nonlinearities can be beneficial for energy harvesting. [DOI: 10.1115/1.4026278]

On the Role of Nonlinearities in Vibratory Energy Harvesting: A Critical Review and Discussion

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Stochastic Processes And Filtering Theory

Damage detection in complicated engineering systems from vibration measurements typically involves the use of algorithms that are built on the principles of bayesian dynamic state estimation. These methods invariably required the solution of the forward problem a fairly large number of times. For complex engineering systems that are numerically modeled using Finite Element (FE), this can be computationally intensive especially when a single FE run for the problem takes a large time. To alleviate this problem, there is a need for the development of Reduced Order Models (ROMs) that significantly reduce the computational cost associated with solving the forward problem, for a given measure without sacrificing the accuracy. The present study discusses three ROM methods with specific reference to a simple problem. These methods include well-known Component Mode Synthesis (CMS) and System Equivalent Reduction Expansion Process (SEREP) which are applicable only for linear systems, as well as Principal Component Analysis (PCA)—the method which is more general and can be used for nonlinear systems as well. A comparison of the performance of all these methods is carried out for a stepped beam. The FE based results obtained from the full model is treated as the benchmark.

Analysis of Stepped Beam Using Reduced Order Models

A nonlinear dynamic model of a small-sag stay cable with an axial support motion is considered. A magnetorheological (MR) damper is employed for semi-active control of cable vibrations. Voltage supplied to the MR damper has been monitored through a two-stage state feedback control design approach. The first stage contains a primary controller, which determines the force required to obtain a desired closed-loop response of the system. In the second stage, an optimal dynamic inversion approach has been used to obtain the amount of voltage to be supplied to the MR damper such that it provides the required control force prescribed by the primary controller. Keywords: nonlinear vibrations, semi-active control, stay-cable vibrations

Semi-Active Control of Stay Cable Vibrations Using Magnetorheological Damper

This manuscript analyzes the performance of a tristable vibration energy harvester under Gaussian white noise excitation. Broadband vibration energy harvesting has attracted significant research attention and is targeted toward obtaining large power output over a wide range of frequencies. Nonlinearity can be introduced into vibration energy harvesting systems through multi-stability. In cantilever-type vibration energy harvesters, multi-stability could be achieved by the introduction of magnetic interactions. When two external magnets are used, the harvester can have up to three stable static equilibrium positions. The harvester with two stable states has been explored widely, both theoretically and experimentally. Recently, the harvester with three stable states is shown to perform better than its bistable counterpart in the presence of a linearly increasing harmonic sweep excitation. Ambient vibrations are random in nature, and the performance of tristable energy harvesters under such excitations needs to be studied. To begin with, we study the performance of tristable energy harvesters under Gaussian white noise excitation through numerical simulations. The simulations show that beyond a certain critical amplitude of excitation, the harvesters undergo inter-well oscillations and harvest more power. This implies that if the variance of the random ambient excitation is known, then the harvester could be optimized so that the mean harvested power is maximized.

Shaikh Faruque Ali

Papers

Analysis of Stepped Beam Using Reduced Order Models

Semi-Active Control of Stay Cable Vibrations Using Magnetorheological Damper

Analysis of Tristable Energy Harvesters Under Random Excitations